k-Hyponormality and n-Contractivity for Agler-Type Shifts
We consider k-hyponormality and n-contractivity (k, n = 1, 2, ...) as "weak subnormalities" for a Hilbert space operator. It is known that k-hyponormality implies 2k-contractivity; we produce some classes of weighted shifts including a parameter for which membership in a certain n-contractive class is equivalent to k-hyponormality. We consider as well some extensions of these results to operators arising as restrictions of these shifts, or from linear combinations of the Berger measures associated with the shifts.
Journal of Operator Theory
Adams, Gregory and Exner, George. "k-Hyponormality and n-Contractivity for Agler-Type Shifts." Journal of Operator Theory (2014) : 585-600.